Reynolds analogy for a shearing granular material

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Abstract
The bulk motion of a granular material affects its apparent thermal as well as its apparent mechanical properties. This paper presents the simultaneous measurements of the apparent viscosity and thermal conductivity for a dry granular material undergoing shear in an annular shear cell. Both properties are seen to vary linearly with the shear rate. As such, it can be argued that both the apparent conductivity and viscosity are proportional to the square root of the granular temperature in exactly the same way as the kinetic theory of gases predicts that the conductivity and viscosity of a perfect gas vary as the square root of the thermodynamic temperature. Thus, analogies can be drawn between the mechanical and thermal behaviour of a granular flow that share much with similar — a.k.a. Reynolds — analogies for both laminar and turbulent flows of simple fluids. However, the results do indicate fundamental differences in the internal transport of heat and momentum. In particular, heat may only be transmitted by the streaming motion of the particles, while momentum may also be exchanged during interparticle collisions.